Gas Laws

Phases of Matter SOLID Definite Shape Definite Volume LIQUID Shape varies depending on container Definite Volume GAS Takes on the shape and volume of the container ENERGY INCREASES

Some Properties of Gases Fill their container completely Easy to compress Diffuse rapidly Exert pressure –Pressure is defined as the number of collisions per unit area

Pressure –force per unit area P = Force/Area Gas molecules –they fill container completely (spread out) –molecules move around and hit sides –collisions with the container are the force that adds up to the be total pressure which that gas exerts

Pressure Can be given in: –atmospheres (atm) –millimeters of mercury (mmHg) –kiloPascals (kPa) You must convert to atm before using the value in an equation 760 mmHg = 1 atm kPa = 1 atm

Measuring Pressure Manometer Before adding gas to flask:After adding gas to flask:

Manometer Example: Which gas is exerting more pressure? AB

Kinetic-Molecular Theory The Nature of Gases: 1.A gas has mass 2.Gas particles are spread far apart 3.Particles are on constant, rapid, random motion 4.Collisions are elastic 5.Energy depends on temperature

Boyle’s Law Pressure and volume of a gas are inversely related (V dec., P inc.; V inc., P dec) PV = k P 1 V 1 = P 2 V 2 (when temp. is constant) (P in atmospheres, V in liters)

Gas Laws Example: A gas in a cylinder with a movable piston occupies 1.2 liters at 1.5 atmospheres of pressure. The piston is moved and the gas now occupies 0.70 liters. Assuming temperature is constant, what will the pressure (in atm) now be in the cylinder? 2.6 atm

Gas Laws Practice: A gas in a cylinder with a movable piston occupies 4.98 liters at 152 kPa of pressure. The piston is moved and the gas now occupies 5.23 liters. Assuming temperature is constant, what will the pressure (in atm) now be in the cylinder? 1.43 atm

Charles’ Law Temperature and Volume are directly related V/T = k V 1 /T 1 = V 2 /T 2 (when pressure constant) (V in liters, T in kelvin) V 1 T 2 = V 2 T 1

Temperature in Kelvin Most of the time temp is given in ˚C temp ˚C = temp K Example Convert 25 ˚C into kelvin

Gas Laws Example: A hot air balloon is filled with 1551 liters of hot air on a morning in which the temperature is 295 K. What would the volume (in liters) of the hot air balloon be if the temperature dropped to 285 K? 1498 L

Gas Laws Example: A hot air balloon is filled with 1551 liters of hot air on a morning in which the temperature is 34 ˚C. What would the volume (in liters) of the hot air balloon be if the temperature dropped to 22 ˚C? 1490 L

Gay-Lussac’s Law Pressure and Temperature are directly related P/T = k P 1 /T 1 = P 2 /T 2 (when volume is constant) (P in atm, T in Kelvin) P 1 T 2 = P 2 T 1

Combined Gas Law P 1 V 1 = P 2 V 2 T 1 T 2 P = pressure in atmospheres (atm) V = volume in liters (L) T = temperature in Kelvin (K)

Gas Laws Example: A sample of oxygen gas occupies 5.2 liters at 29ºC and 1.5 atm. What would be the volume (in liters) at 35ºC and 0.97 atm? 8.2 L

Ideal Gas Law Describes the behavior of an ideal gas Real gases basically behave like ideal gases except at very low temperatures and at very high pressures PV = nRT P is pressure in atm V is volume in L n is number of moles of gas in mol R is the gas constant in atmL/molK T is the temperature in K R = atmL/molK

Gas Laws Example How many moles of helium are present in a 35.2 L tank at 45˚C at a pressure of 1635 kPa? (R = atmL/molK) 21.8 moles

Gas Laws Example How many liters of hydrogen are present if 3.52 moles of hydrogen are kept at 299K at a pressure of 1635 kPa? (R = 8.31 kPaL/molK) 5.35 liters

DID we keep partial pressures

Dalton’s Law of Partial Pressures The sum of the partial pressures of all the components in a gas mixture is equal to the total pressure of the gas mixture P T = p a + p b + p c + …

Dalton’s Law of Partial Pressures Example: A mixture of carbon dioxide and oxygen gases is contained at 25˚C and mmHg. The carbon dioxide gas exerts 34.6 mmHg pressure. What is the partial pressure (in mmHg) of the oxygen gas? mmHg

Dalton’s Law of Partial Pressures Example: Carbon dioxide exerts a pressure of 0.15 atm in a container. In the same container, helium gas exerts a pressure of 0.22 atm and oxygen gas exerts a pressure of 0.39 atm. What is the total pressure (in atm) of the mixture of gases in the container? 0.76 atm

References